i cant seem to figure this out

Tutors, sign in to answer this question.

What is m^3 – 3m^2 = 5m – 15 factored?

It's interesting that the problem was posed this way because you might notice that you can use the Distributive Property on both sides:

m^2(m – 3) = 5(m – 3)

At this point you might decide to say "If m ≠ 3 then I can divide both sides by (m–3) to get m^2 = 5, where m = ±√(5) are the only two answers."

However, if instead you subtracted 5(m – 3) from both sides:

m^2(m – 3) – 5(m – 3) = 0

and used the Distributive Property:

(m – 3)(m^2 – 5) = 0

Substitute (√(5))^2 for 5:

(m – 3)(m^2 – (√(5))^2) = 0

Use Difference of Squares:

(m – 3)(m + √(5))(m – √(5)) = 0

That's the answer to, "What is m^3 – 3m^2 = 5m – 15 factored?"

But now, using the Zero Product Property, you can find the values of m that make it true:

(m – 3) = 0 ==> m = 3

(m – √(5)) = 0 ==> m = + √(5)

(m + √(5)) = 0 ==> m = – √(5)

Hi Tabalina;

m^3-3m^2=5m-15

Let's bring everything to one side...

m^{3}-3m^{2}-5m+15=0

For the FOIL...

FIRST must be (m^{2})(m)=m^{3}

(m^{2}...)(m...)

OUTER must be (-3)(m^{2})=-3m^{2}

(m^{2}...)(m-3)

INNER must be (-5)(m)=-5m

(m^{2}-5)(m-3)

LAST must be (-5)(-3)=15

0=(m^{2}-5)(m-3)

Either or both parenthetical equation(s) must equal zero...

0=m^{2}-5.........0=m-3

5=m^{2}............3=m

+/- √5=m

Please remember that - √5, when squared, produces the same result as +√5, when squared.

There are three answers...

m=-√5, +√5 and 3

Richard P. | Fairfax County Tutor for HS Math and ScienceFairfax County Tutor for HS Math and Sci...

The first step is to reorganize the equation to get a zero on the right hand side

m^{3} - 3m^{2} - 5 m + 15 = 0

The cubic expression on the left hand side can be factored by a method called factoring by grouping.

This method does not always work, but is very good when it does.

Step 1: pull a factor of m^{2} out of the first two terms m^{2} (m -3)

Step 2: pull a factor of -5 out of the last two terms -5(m-3)

Step 3: {this is the good part} notice that in both steps 1 and 2 we got a factor of (m-3)

Step 4: take advantage of this good fortune to write the whole expression as (m-3) ( m^{2} -5)

This ends the factor by grouping part

Step 5: m^{2} -5 factors as (m- sqrt(5) ) (m + sqrt(5))

Final answer (m-3) (m - sqrt(5)) ( m+ sqrt(5)) = 0

So the solutions to the problem are

m = 3

m = - sqrt(5)

m = + sqrt(5)

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Lisa T.

Experienced Tutor, Specializing in Math, Science and English

$11.25 per 15 min

View Profile >

Kevin T.

A Laid Back Tutor who Specializes in Math, Science, and Test Prep

$11.25 per 15 min

View Profile >

Colin B.

Experienced Math Tutor

$11.25 per 15 min

View Profile >